Grothendieck-Serre duality and theta-invariants on arithmetic surfaces

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Abstract


In the paper, a description of the Grothendieck-Serre duality on an arithmetic surface by means of fixing a horizontal divisor is given and this description is applied to the generalization of theta-invariants.


About the authors

D. V. Osipov

Steklov Mathematical Institute of Russian Academy of Sciences

Author for correspondence.
Email: d_osipov@mi-ras.ru

Russian Federation, 8, Gubkina street, Moscow, 117966

References

  1. Bost J.-M. Theta Invariants of Euclidean Lattices and Infinite Dimensional Hermitian Vector Bundles over Arithmetic Curves. arxiv: 1512.08946
  2. Hartshorne R. Residues and Duality. Lecture Notes of a Seminar on the Work of A. Grothendieck, Given at Harvard 1963/64. With an Appendix by P. Deligne. Lecture Notes in Mathematics. № 20. B.; N.Y.: Springer-Verlag, 1966.
  3. Liu Q. Algebraic Geometry and Arithmetic Curves. Translated from the French by Reinie Erné. Oxford Graduate Texts in Mathematics, 6. Oxford Science Publications. Oxford: Oxford University Press, 2002.
  4. Deligne P. Le Déterminant de la Cohomologie. Current Trends in Arithmetical Algebraic Geometry (Arcata, Calif., 1985), 93-177. Contemp. Math., 67. Amer. Math. Soc., Providence (RI), 1987.
  5. Осипов Д. В., Паршин А. Н. Гармонический анализ на локальных полях и пространствах аделей // Изв. РАН. Сер. матем. 2011. Т. 75. № 4. С. 91-164.
  6. Осипов Д. В. Арифметические и адельные факторгруппы // Изв. РАН. Сер. матем. 2018. Т. 82. № 4. С. 178-198.

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